Exploration of the ACOPF Feasible Region for the Standard IEEE Test Set Optimal Power Flow - Optimal Power Flow Paper 6

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1、OptimalPowerFlowPaper6StaffpaperbyAaronSchecterRichardPO’NeillFebruary2013ExplorationoftheACOPFFeasibleRegionfortheStandardIEEETestSetOptimalPowerFlowPaper6AaronSchecterandRichardPO’Neillaschec@gmail.comrichard.oneill@ferc.govFebruary2013AbstractandExecutiveSummaryThegoalofourinvesti

2、gationistogainsomeperspectiveonhownon‐convexthefeasibleregionoftheAlternatingCurrentOptimalPowerFlowሺACOPFሻproblemis.First,wewilldevelopametricforcomparinghowinfeasibledifferentsolutionsare.Theset‐upforthisexaminationwillbetogenerateconvexcombinationsoffeasiblepoints,anddeterminehow“

3、far”thesenewpointsarefromthefeasibleregion.Weproposeametricbasedontherelativetwonorm.Thisvaluewillbecomparedovervariousregionsaroundtheoptimalsolution.Second,wewouldliketodeterminehowelastictheareaaroundtheglobaloptimumis;inotherwords,wewilldeterminethelargestrangeofvaluestheoptimiza

4、tionvariablescantake,givenasmallperturbationfromtheglobalsolution.Indoingso,wewillfindtheelasticityofalloptimizationvariables,whichcouldgiveusinsightintothestructureofthefeasibleregion.Finally,wewillexaminethetwodimensionalrelationshipsbetweentheoptimizationvariablesandtheobjectivefu

5、nctionvalue.IndexTerms—OptimalPowerFlow,FeasibleRegion,SolutionSpace,LocalSolutions,ElasticityDisclaimer:TheviewspresentedarethepersonalviewsoftheauthorsandnottheFederalEnergyRegulatoryCommissionoranyofitsCommissioners.TableofContentsNomenclature11.Introduction12.FeasibleRegionOfTheA

6、copfProblemAcFlowEquations23.ElasticityNearTheOptimalSolution34.Fixed‐VariableOptimizationacopfFormulation55.Conclusions7References71NOMENCLATUREIngeneral,itcanbeshownthattherearealargenumberofIndicesphysicallyfeasibleloadflowsolutions[5]andthusnumerousn;mNodeslocaloptima.Asaresult,th

7、eissueofconvexitybecomeskLinesimportantforbothaccuracyandreliabilitypurposes.InthisgGeneratorspaper,weestablishsomebasiccharacteristicsoftheseproblemsusingtheIEEEstandardtestsuite[1]andfurthercontributetoVariablesthediscussionoftheirstructure.vnVoltageatBusnThefirstsegmentofourinvesti

8、gationfocuse